The mission said in a statement Pope Benedict XVI had accepted Wielgus's resignation.
Wielgus was appointed by the pope last month to succeed anticommunist Jozef Cardinal Glemp.
According to the statement, Glemp will temporarily return to the position.
The controversy surrounding Wielgus emerged after a Polish newspaper published allegations that he had been an informant for the communist secret services.
Wielgus on January 5 admitted to having had contact with the secret services, but he refuted charges that he had spied upon his ecclesiastical colleagues.
(compiled from agency reports)